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Grades 9–12 · Language

How can language frame the same numbers?

The same record can sound different when it is described in different ways. If 80 of 100 trials succeeded, then 20 of those same 100 trials failed. A success frame brings the 80 successes forward; a failure frame brings the 20 failures forward. The underlying counts have not changed.

L08 visual explanationThe same complete record contains 80 successful and 20 failed trials out of 100; every trial has one outcome. 80% succeeded. Both percentages use the same denominator and period. A qualifier changes emphasis, not these counts. No audience response is measured.Same record, different wording100 trials in one recorded test80 succeeded20 failed80% succeeded.Read the record and its denominator.80% success = 20% failure here.

In the diagramSame record, different wording100 trials in one recorded test80 succeeded20 failed80% succeeded.Read the record and its denominator.80% success = 20% failure here.

The bar represents one record of 80 successes and 20 failures. “80% succeeded” and “20% failed” are equivalent descriptions of these same 100 trials.

The comparison works because both descriptions concern the same trials, the same period and the same definition of success. Eighty percent successful and twenty percent unsuccessful are complementary descriptions under those conditions. If the groups or definitions differ, the percentages may no longer describe the same evidence.

Words such as only or as many as can add an evaluation to a count. Only twenty failures and as many as twenty failures point toward different judgments about the same number. Whether twenty is acceptable requires some further basis for comparison, such as the purpose of the trials or the consequences of failure.

Framing therefore changes what a description emphasizes without necessarily changing what happened. It can influence how a reader interprets a result, but a particular effect on a particular audience needs evidence of its own. Keeping the denominator, definitions and wording visible helps separate the measured record from the interpretation offered.

About this explanation

Starting knowledge: Calculate simple percentages and complements; distinguish a visible numerical statement from an unsupported universal audience prediction.

Sources

  • Amos Tversky and Daniel Kahneman, Science — The Framing of Decisions and the Psychology of Choice (1981)
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